Numerical range, numerical radii and the dynamics of a rational function

Melo, Helena Sousa; Cabral, João

http://hdl.handle.net/10400.3/2519

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Authors

Melo, Helena Sousa

Cabral, João

Abstract(s)

Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps. In this study we use the family of maps f(x) = (x^2-a)/(x^2-b), making some associations with the matrix A of its coefficients. Calculating the numerical range W(A), the numerical radii r(A) and br(A), the boundary of the numerical range @W(A), powers and iterations, we found relations very interesting, especially with the entropy of this maps.

Description

Texto publicado no seguimento da comunicação apresentada na "Twelfth International Conference on Difference Equations and Application", no Instituto Superior Técnico em Lisboa, 23-27 Julho 2007.

Keywords

Numerical Range Rational Function

URI

http://hdl.handle.net/10400.3/2519

Citation

Melo, Helena S., Cabral, João (2010). "Numerical range, numerical radii and the dynamics of a rational function". In Elaydi, Saber N. et al. (Eds.), «Discrete Dynamics and Difference Equations» (World Scientific), pp 336-344. http://dx.doi.org/10.1142/9789814287654_0027.